A complete workout for your arms must comprise exercises for your biceps and triceps muscles. These two groups of muscles are located at the front and back of your upper arms, respectively. They act in opposition. The biceps let you bend your arms while the triceps straighten them. These are simple movements that can be translated into weight training exercises: biceps curls and triceps extensions. By doing these types of movements, you will build bigger and stronger arms.
To exercise your biceps, all you need is a barbell and/or pair of dumbbells. With these free weight pieces of equipment, you can do the biceps curl exercise and its many variants. Grasp the barbell or dumbbell with a palms-up shoulder-width apart grip, stand up straight with feet shoulder-width apart and position elbows by your sides. Bend your arms to raise the weights up to your shoulders, squeeze your biceps and then return the weights down. To focus on the inside of your biceps, do wide-grip barbell curls, with your hands more than shoulder-width apart holding the bar. You can also focus on the outside of your biceps by utilizing a narrow grip less than shoulder-width apart. This exercise variant is called close-grip barbell curls. One more variation you can perform, but with dumbbells, is the seated dumbbell curl. By sitting down, you prevent cheating via rocking your back to lift the weights. The seated position forces you to use stricter form, which is a much safer way to do the exercise.
Target Your Triceps
Similar to biceps training, you can work on your triceps muscles with just a barbell and dumbbells. The core triceps exercise you should perform is the triceps extension movement. Perform this exercise by standing up straight holding the barbell or dumbbells over your head with your arms straight. Bend your arms as much as you can in a slow and controlled motion and then extend your arms up to the beginning position. You can do this exercise one hand at a time with a dumbbell to better focus on side of your triceps. Two other exercise variations that will help you build your triceps are the seated overhead triceps extension and the lying triceps extension. The seated version increases stability of the exercise, allowing you to use more weight, so you better challenge your muscles. The lying-down version, on the other hand, reduces the pressure of the exercise on your spine due to your back being rested on the bench -- so, it is a safer form of the movement.
Don't Settle for Less
A complete workout for your arms must include enough sets to sufficiently build your arms. Do four of the aforementioned exercises, two biceps and two triceps exercises, per workout. For each exercise, perform four sets of 12 reps using as much weight as you can safely handle.
Better Safe Than Sorry
Begin each arm workout with a 10-minute warmup consisting of jumping rope, jumping jacks and pushups. Keep the intensity low to moderate, as you are just warming your muscles up during this phase, rather than trying to break any personal records. Save your energy for the actual workout. Once you finish your arm workout, follow up with a 10-minute cool down on the treadmill or stepmill to return your body closer to its natural state at rest.